Colorectal cancer is the third-most commonly diagnosed cancer in the world. Conventional optical colonoscopy (OC) is used for screening precancerous polyps, but it requires an invasive operation and can cause harm and pain to patients. Virtual colonoscopy (VC), also called computerized tomography (CT) colonography provides a more comfortable and non invasive alternative diagnosis tool. VC requires extraction of a 3D colon inner wall surface from CT scans of the abdomen, followed by a radiologist “flying” through the virtual 3D colon tunnel to locate precancerous polyps and cancer. The colon is a long and convoluted tube structure, so VC can be time-consuming and is difficult to perform if the colon is occluded.
Additionally, in general computer vision, efficient shape representations for surfaces can be used to effectively deal with shape analysis problems, such as shape indexing, matching, recognition, classification, and registration. Canonical surface mappings such as conformal mappings, provide shape representations with good properties, which are global and intrinsic and have the guarantee of existence and uniqueness.
In the past decade, much research has focused on conformal mapping methods, including least square conformal maps, differential forms, and discrete curvature flows. The surface uniformization theorem states that any arbitrary surface can be conformally mapped to one of three canonical spaces: the unit sphere; the Euclidean plane; or the hyperbolic disk.